CN107102298B - Radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method - Google Patents
Radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses a kind of, and the radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method, its thinking are as follows: determine uniform circular array, the uniform circular array includes M array element, there are Q signal sources in uniform circular array setting range, Q signal source emits Q incoming signal to uniform circular array, and the Q incoming signal includes 1 desired signal and Q-1 interference signal；It obtains the sample covariance matrix R of uniform circular array and carries out feature decomposition, obtain M characteristic value；It calculates the signal MUSIC that incident direction is (θ, φ) to compose, then sets the mutual coupling matrix setup values of uniform circular array, and then obtain the Q azimuth initial value of Q incoming signal, and respectively obtain the final mutual even matrix of uniform circular arrayWith the final bearing of Q incoming signalThen the interference plus noise covariance matrix of uniform circular array after reconstructing is calculatedAnd then the weight vector of the adaptive beam former of uniform circular array is obtained, complete the uniform circular array interference plus noise covariance matrix reconstruct based on iteration mutual coupling calibration.
Description
Technical field
The invention belongs to conformal array antenna beam-forming technology field, in particular to a kind of thunder based on iteration mutual coupling calibration
Beamforming Method is reconstructed up to covariance matrix, leads to adaptive wave more by force suitable for solving desired signal power sample
The problem of beamformer robustness declines, and consider the problems of that Beam-former performance declines when mutually even effect, and examining
The steady performance of Beam-former is improved while considering mutual coupling.
Background technique
Conformal array does not interfere with electromagnetism concealment, big scanning angle, small load weight and flying body due to it
The advantages that air force flow field and be widely used；It is researched and developed however, conformal array beams form technology in theory
Application aspect all suffers from several problems.Firstly, traditional beam-forming technology has steady performance is insufficient in the actual environment to lack
It falls into, is still remained when this Application of defect is to conformal array；In addition, the signal of array antenna received is in receiving unit internal transmission
When, the mutual even effect between array element can not be ignored.And the array element distribution of conformal array complexity, it increases and its electromagnetic property is carried out accurately
The difficulty of analysis and modeling, so that the mutual coupling calibration of conformal array is very difficult.Therefore in the premise for giving full play to conformal array advantage
Under, steady beamforming algorithm is designed, mutual coupling factor is broken through and the limitation of Beam-former is a problem to be solved.
The theoretical research of Adaptive beamformer technology originates in the 1960s.1969, Capon proposed minimum side
Response (MVDR) criterion that difference is undistorted, the criterion minimize the output power of array while guaranteeing it is expected signal gain, are
Beam-former inhibits interference to provide theoretical basis.In the 1970s, researcher proposes sample matrix inversion (SMI)
Algorithm, the algorithm estimate interference plus noise covariance matrix using array received signal snap, and inhibition that can be adaptive is interfered
Signal.1974, Brennan et al. was deduced the probability density function of the output Signal to Interference plus Noise Ratio of SMI beamforming algorithm, gave
The performance of adaptive algorithm and the relationship of number of training are gone out.
In numerous practical application areas, the performance of adaptive beam former will receive the influence of various error components,
Such as signal observation error, receiving channel error, sensor position uncertainties etc., these errors will cause array antenna received signals guiding
Vector mismatch causes beamforming algorithm performance to decline；And when containing desired signal in sample snap, the mistake of steering vector
The performance influence for matching adaptive beam former is especially pronounced.
In 1991, Benjamin Friedlander and W Anthony J.Weiss proposed that one kind exists between array element
DOA estimation method when mutual coupling can accurately estimate the mutual coupling between the direction of arrival DOA of signal and uniform circular array,
But it should there are DOA estimation methods when mutual coupling not to apply in Adaptive beamformer technical field between array element；2012
Year, Gu proposes a kind of Beamforming Method based on interference plus noise covariance matrix reconstruct, after this method is using reconstruct
Covariance matrix replaces being calculated adaptive weight vector by desired contamination sampling covariance matrix, although in desired signal power
There is preferable performance when stronger, but this method has following two: first in practical applications, this method requires battle array
Column configuration be it is accurately known, the error uniquely allowed is observation angle error, the performance sharp fall when considering mutually even effect；
Second, this method computation complexity when reconstructing interference plus noise covariance matrix is very big, so that the real-time system of algorithm
About.
Summary of the invention
In view of the above shortcomings of the prior art, it is an object of the invention to propose a kind of radar based on iteration mutual coupling calibration
Covariance matrix reconstructs Beamforming Method, this kind reconstructs Wave beam forming side based on the radar covariance matrix of iteration mutual coupling calibration
Method is iterated estimation to the incident angle of signal and the mutual coupling matrix of uniform circular array, in conjunction with interference plus noise covariance matrix weight
Structure method completes the reconstruct of interference plus noise covariance matrix and it is expected the amendment of steering vector, obtains a kind of in array element presence
More steady Beam-former under conditions of mutual coupling.
In order to achieve the above objectives, the present invention is realised by adopting the following technical scheme.
A kind of radar covariance matrix reconstruct Beamforming Method based on iteration mutual coupling calibration, comprising the following steps:
Step 1, uniform circular array is determined, which includes M array element, and there are Q letters in uniform circular array setting range
Number source, Q signal source emit Q incoming signal to uniform circular array, and the Q incoming signal is a comprising 1 desired signal and Q-1
Interference signal；
The sample covariance matrix R of uniform circular array is obtained, and the sample covariance matrix R of the uniform circular array is carried out special
Sign is decomposed, and M characteristic value is obtained；M, Q is respectively the positive integer for being greater than 0, and Q > 1, M indicate the element number of array that uniform circular array includes,
The characteristic value number value obtained after carrying out feature decomposition with the sample covariance matrix R to uniform circular array is equal；
Step 2, it calculates the signal MUSIC that incident direction is (θ, φ) to compose, at the beginning of the mutual coupling matrix for then setting uniform circular array
Initial value, and then the Q azimuth initial value of Q incoming signal is obtained, respectivelyq∈{0,1,
2 ..., Q-1 },Indicate the azimuth initial value of the q+1 incoming signal；
Initialization: enabling k indicate kth time amendment, and the initial value of k is 1；The mutual coupling matrix of uniform circular array after enabling kth time correct
For Ck, and using Q azimuth initial value of Q incoming signal as the azimuth angle theta of Q incoming signal after the 0th amendment0；Setting
The mutual coupling matrix setup values of uniform circular array are C0, C0=IM, IMIndicate that M × M ties up unit matrix；
Step 3, according to the mutual coupling Matrix C of uniform circular array after kth time amendmentkWave is carried out respectively to Q incoming signal up to side
To estimation, incident direction is (θ after obtaining kth time amendmentk, φ) signal MUSIC compose PMUSIC(θk, φ) and kth time amendment
The azimuth of Q incoming signal afterwards；
Step 4, successively obtain the MUSIC spectrum inverse of Q incoming signal after kth time amendment and JckDefinition and meter
Formula, and then the mutual coupling Matrix C of uniform circular array after kth time amendment is calculatedk；
Step 5, k is enabled to add 1, return step 3, until Jck-Jc(k-1)< △, then correcting iteration terminates, Jc(k-1)Indicate kth -1
The sum of the MUSIC spectrum inverse of Q incoming signal after secondary amendment, △ indicate the threshold value of setting, and respectively stop amendment iteration
The mutual coupling Matrix C of uniform circular array after corresponding kth time is corrected when onlyk, it is denoted as the final mutual even matrix of uniform circular arrayIt will amendment
The azimuth of Q incoming signal, is denoted as the final bearing of Q incoming signal after corresponding kth time is corrected when iteration stopping
Step 6, according to the final mutual even matrix of uniform circular arrayWith the final bearing of Q incoming signalIt calculates
The interference plus noise covariance matrix of uniform circular array after to reconstruct
Step 7, the vector that is eventually led to that desired signal is calculated isAnd according to uniform circular array after reconstruct
Interference plus noise covariance matrixThe weight vector that the adaptive beam former of uniform circular array is calculated is w, and then complete
At the Wave beam forming design of the uniform circular array interference plus noise covariance matrix reconstruct based on iteration mutual coupling calibration.
Beneficial effects of the present invention: first, the present invention using DOA and uniform circular array mutual coupling matrix iteration estimation method compared with
Accurately to estimate indispensable two parameters in the interference plus noise covariance matrix reconstruct under mutual coupling, i.e.,
The mutual coupling matrix of nicely rounded battle array and the azimuth of interference signal, so that the reconstruct of interference plus noise covariance matrix sufficiently carries mutually
Coupling information improves the robustness of the Beam-former under mutual coupling；Second, the present invention is used to be taken in interference angular regions
Discrete point rather than the method for integral reconstructs interference covariance matrix, reduce computation complexity, improve the real-time of algorithm.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is that a kind of radar covariance matrix based on iteration mutual coupling calibration of the invention reconstructs Beamforming Method process
Figure；
Fig. 2 is that there are the method for the present invention performances when observation error with signal-to-noise ratio (SNR) change curve under array mutual-coupling condition；
Fig. 3 (a) be under array mutual-coupling condition there are observation error and when input signal-to-noise ratio is 20dB the method for the present invention performance with sample
This number change curve；
Fig. 3 (b) be under array mutual-coupling condition there are observation error and when input signal-to-noise ratio is -5dB the method for the present invention performance with sample
This number change curve；
The method of the present invention performance is with SNR change curve when Fig. 4 is no errors of measurements under array mutual-coupling condition；
Fig. 5 (a) be under array mutual-coupling condition no errors of measurements and when input signal-to-noise ratio is 20dB the method for the present invention performance with sample
Number change curve；
Fig. 5 (b) be under array mutual-coupling condition no errors of measurements and when input signal-to-noise ratio is -5dB the method for the present invention performance with sample
Number change curve.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Referring to Fig.1, Wave beam forming side is reconstructed for a kind of radar covariance matrix based on iteration mutual coupling calibration of the invention
Method flow chart；Wherein the radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method, including following step
It is rapid:
Step 1, uniform circular array is determined, which includes M array element, obtains the sample covariance matrix of uniform circular array
R carries out feature decomposition to the sample covariance matrix R of the uniform circular array, obtains M characteristic value；Wherein M is just greater than 0
Integer.
Specifically, it is determined that uniform circular array, which includes M array element, and there are Q letters in uniform circular array setting range
Number source, Q signal source emit Q incoming signal to uniform circular array, and the Q incoming signal is a comprising 1 desired signal and Q-1
Interference signal；For within uniform circular array S km, S is the positive integer greater than 0 in the setting range；S takes in the present embodiment
Value is 100.
Q incoming signal is φ, φ={ φ relative to the pitch angle of uniform circular array0,φ1,…,φq,…,φQ-1, q ∈
{ 0,1 ..., Q-1 }, φqIndicate pitch angle of the q+1 incoming signal relative to uniform circular array, and φ0、φ1、…、φq、…、
φQ-1Value difference is equal；φ0Indicate pitch angle of the desired signal relative to uniform circular array, Q-1 interference signal is relative to equal
The pitch angle of nicely rounded battle array is respectively φ1、φ2、…、φQ-1。
The echo data that uniform circular array receives is obtained, and the echo data that the uniform circular array receives is carried out from phase
Pass processing, obtains the sample covariance matrix R of uniform circular array.
Known desired number is 1, interference signal number is Q-1 and Q incoming signal is relative to uniform circular array
Pitch angle be φ under the premise of, feature decomposition is carried out to the sample covariance matrix R of uniform circular array, obtains M characteristic value；By
It is M in the element number of array of uniform circular array, then the characteristic value number obtained after feature decomposition is also M.
The M characteristic value obtained after feature decomposition is sorted from large to small, and respectively by the M after sorting from large to small
Preceding Q characteristic value is denoted as Q big characteristic values in a characteristic value, remaining M-Q characteristic value is denoted as M-Q small characteristic values；By preceding Q
The corresponding feature vector of a big characteristic value, as desired signal plus interference space, by the corresponding feature of M-Q small characteristic value to
Amount, is denoted as noise subspace, then carries out feature decomposition, decomposed form to the sample covariance matrix R of uniform circular array are as follows:
Wherein, R is the sample covariance matrix of uniform circular array, and dimension is M × M；ΛSIIt is respectively pair for Q big characteristic value
The diagonal matrix that angle element is formed, USIThe desired signal formed for the corresponding feature vector of Q big characteristic value adds interference space,
ΛNIt is respectively the diagonal matrix that diagonal element is formed, U for M-Q small characteristic valuesNFor the corresponding feature vector of M-Q small characteristic value
The noise subspace of formation, subscript H indicate that conjugate transposition operation, M, Q are respectively the positive integer for being greater than 0, M > Q；M indicates nicely rounded
The element number of array that battle array includes carries out the characteristic value number obtained after feature decomposition with the sample covariance matrix R to uniform circular array
Value is equal.
Step 2, it calculates the signal MUSIC that incident direction is (θ, φ) to compose, at the beginning of the mutual coupling matrix for then setting uniform circular array
Initial value, then incident direction is that the signal MUSIC of (θ, φ) has composed an initial estimate；By the mutual coupling matrix of uniform circular array
Initial value substitutes into the signal MUSIC that incident direction is (θ, φ) and composes PMUSICIn (θ, φ) expression formula, and in setting azimuth coverage
Interior search MUSIC spectral peak, and then the Q azimuth initial value of Q incoming signal is obtained, respectively
Specifically, the incident direction is that the signal MUSIC of (θ, φ) composes PMUSIC(θ, φ), expression formula are as follows:
Wherein, θ indicates the azimuth of Q incoming signal, and φ indicates pitching of the Q incoming signal relative to uniform circular array
Angle, a (θ, φ) are the signal guide vector that incident direction is (θ, φ), and C is the mutual coupling matrix of uniform circular array, and uniform circular array
Mutual coupling Matrix C is unknown；UNFor the noise subspace that the corresponding feature vector of M-Q small characteristic value is formed, subscript H is indicated altogether
The operation of yoke transposition.
Set the mutual coupling matrix setup values C of uniform circular array0, C0=IM, IMIndicate that M × M ties up unit matrix；By uniform circular array
Mutual coupling matrix setup values C0It substitutes into the signal MUSIC that incident direction is (θ, φ) and composes PMUSICIn (θ, φ) expression formula, and at 0 °
MUSIC spectral peak is searched in 180 ° of azimuth coverages, and then obtains the Q azimuth initial value of Q incoming signal, respectivelyIndicate the azimuth initial value of the q+1 incoming signal；Wherein,
It sets in azimuth coverage as within the scope of 0 ° to 180 °.
Initialization: enabling k indicate kth time amendment, and the initial value of k is 1；And by Q azimuth initial value of Q incoming signal
Azimuth angle theta as Q incoming signal after the 0th amendment0；The mutual coupling matrix setup values of uniform circular array are set as C0, C0=IM, IM
Indicate that M × M ties up unit matrix.
Step 3, after the completion of feature decomposition, in the case where considering uniform circular array mutual coupling, uniform circular array after kth time amendment is enabled
Mutual coupling matrix be Ck, and according to the mutual coupling Matrix C of uniform circular array after kth time amendmentkQ are entered using MUSIC Power estimation method
It penetrates signal and carries out direction of arrival (DOA) estimation respectively, incident direction is (θ after obtaining kth time amendmentk, φ) signal MUSIC spectrum
PMUSIC(θk,φ)。
Specifically, in the case where considering uniform circular array mutual coupling, according to the mutual coupling Matrix C of uniform circular array after kth time amendmentk
Direction of arrival (DOA) is carried out to incident desired signal and Q-1 interference signal using MUSIC Power estimation method to estimate, is calculated
Incident direction is (θ after obtaining kth time amendmentk, φ) signal MUSIC compose PMUSIC(θk, φ), expression formula are as follows:
Wherein, θkIndicate the azimuth of Q incoming signal after kth time is corrected, φ indicates Q incoming signal relative to uniform
The pitch angle of circle battle array, a (θk, φ) be incident direction be (θk, φ) signal guide vector, CkFor uniform circular array after kth time amendment
Mutual coupling matrix, and the mutual coupling matrix of uniform circular array is unknown after kth time amendment；UNFor the corresponding spy of M-Q small characteristic value
The noise subspace that vector is formed is levied, subscript H indicates conjugate transposition operation.
The mutual coupling Matrix C of uniform circular array is unknown after being corrected due to kth time, and incident direction is (θk, φ) signal
MUSIC composes PMUSIC(θk, φ) and it can not calculate, then desired signal and the direction of arrival (DOA) of interference signal are exactly unknown.
Set kth time amendment is searched in azimuth coverage after incident direction as (θk, φ) signal MUSIC compose PMUSIC
(θk, φ) MUSIC spectral peak, the azimuth for obtaining Q incoming signal after kth time amendment is θk, θk={ θ0k,θ1k,…,
θqk,…,θ(Q-1)k, q ∈ { 0,1 ..., Q-1 }, θqkIndicate the azimuth of the q+1 incoming signal after kth time is corrected；θ0kIt indicates
The azimuth of desired signal, θ after kth time amendment1k,θ2k,…,θ(Q-1)kFor the orientation of Q-1 interference signal after kth time amendment
Angle；Wherein, within the scope of 0 ° to 180 ° in setting azimuth coverage.
Step 4, define Q incoming signal after kth time amendment MUSIC spectrum it is reciprocal and for Jck, by step 3 it is found that
The mutual coupling matrix of uniform circular array is equal with the mutual coupling matrix value of actual uniform circular array after kth time amendment, then kth time amendment
Afterwards the MUSIC spectrum of Q incoming signal it is reciprocal and JckWith minimum value；If the mutual coupling square of uniform circular array after kth time amendment
Battle array is unequal with the mutual coupling matrix value of actual uniform circular array, then the MUSIC spectrum of Q incoming signal is fallen after kth time amendment
Several and JckThere is no minimum value；So at Q azimuth of Q incoming signal after having obtained kth time amendment, the is allowed
After k amendment the MUSIC spectrum inverse of Q incoming signal and JckValue is minimum, and then is calculated after kth time amendment uniformly
The mutual coupling Matrix C of circle battle arrayk。
Step 4 specifically includes following sub-step:
The mutual coupling Matrix C of uniform circular array after (4a) is corrected according to kth timek, define after kth time amendment Q incoming signal
MUSIC spectrum it is reciprocal and be Jck, define expression formula are as follows:
Wherein,Indicate that incident direction isSignal guide vector, φqIndicate the q+1 incident letter
Pitch angle number relative to uniform circular array,Q+1 enter after expression kth time amendment
The azimuth of signal is penetrated, | | | |2Indicate the squared operation again later of modulus value；CkFor the mutual coupling square of uniform circular array after kth time amendment
Battle array, UNFor the noise subspace that the corresponding feature vector of M-Q small characteristic value is formed, subscript H indicates conjugate transposition operation.
Then by step 3 it is found that working as the mutual coupling matrix initial estimate and actual uniform circular array of the uniform circular array of setting
Mutual coupling matrix value is unequal, then after kth time amendment the MUSIC spectrum inverse of Q incoming signal and JckThere is no minimum value；That
In the case where Q azimuth estimated value of Q incoming signal after having obtained kth time amendment, make Q after kth time amendment a
The MUSIC spectrum of incoming signal, the mutual coupling matrix of Lai Xiuzheng uniform circular array minimum with value reciprocal, i.e. solution kth time amendment
Afterwards the MUSIC spectrum of Q incoming signal it is reciprocal and JckThe mutual coupling square of uniform circular array after corresponding kth time is corrected when value minimum
Battle array.
(4b) is since the mutual coupling matrix of uniform circular array is with some special properties: first, the mutual coupling matrix of uniform circular array
It is a symmetrical matrix；Second, the adjacent two array element distance of uniform circular array is bigger, and mutual impedance each other is with regard to smaller；
Third, the mutual impedance for the array element that the array element that the geometry of uniform circular array closure, i.e. number are 2 is 1 to number, is 1 with number
Array element to number be 2 array element mutual impedance value it is equal.
Based on the above characteristic, the mutual coupling Matrix C of uniform circular array after kth time amendmentkIt is a multiple Cyclic Symmetry matrix, it can be with
By the mutual coupling Matrix C of uniform circular array after kth time amendmentkPreceding L in the first rowCA element is completely determining,
Indicate downward floor operation；And determine the mutual coupling Matrix C of uniform circular array after kth time amendmentkIt is (θ with incident directionk, φ)
Signal guide vector a (θk, φ) product, be equivalent to incident direction be (θk, φ) signal guide vector a (θk, φ) in M
M × L of a element compositionCTie up matrix Q [a (θk, φ)] mutual coupling Matrix C with uniform circular array after kth time amendmentkMiddle the first row
Preceding LCThe L of a complete composition of elementC× 1 dimensional vector ckProduct, i.e. Cka(θk, φ) and=Q [a (θk,φ)]ck。
Wherein, ckFor the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe preceding L of middle the first rowCThe L of a element compositionC×
1 dimensional vector,cdkUniform circular array after expression kth time amendment
Mutual coupling Matrix CkThe d+1 element of middle the first row, subscript T indicate transposition operation.
Incident direction is (θk, φ) signal guide vector a (θk, φ) in M element composition M × LCTie up matrix Q [a
(θk, φ)] by the revised one M × L of kth timeCTie up matrix Q1k, kth time revised two M × LCTie up matrix Q2k, kth time
Revised three M × LCTie up matrix Q3kWith the revised four M × L of kth timeCTie up matrix Q4kAddition obtains, i.e. Q [a (θk,
φ)]=Q1k+Q2k+Q3k+Q4k, the revised one M × L of kth timeCTie up matrix Q1k, kth time revised two M × LCTie up square
Battle array Q2k, kth time revised three M × LCTie up matrix Q3kWith the revised four M × L of kth timeCTie up matrix Q4kRespectively by incidence
Direction is (θk, φ) signal guide vector a (θk, φ) in element constitute, wherein kth time revised one M × LCTie up square
Battle array Q1kIn r row, h column element be Q1(r,h)k, the revised two M × L of kth timeCTie up matrix Q2kIn r' row, h' column member
Element is Q2(r',h')k, the revised three M × L of kth timeCTie up matrix Q3In r " row, h " column element be Q3(r”,h”)k, kth is secondary to repair
Four M × L after justCTie up matrix Q4In r " ' row, h " ' column element is Q4(r”',h”')k, expression formula is respectively as follows:
Wherein, r ∈ { 1,2 ..., row1k, h ∈ { 1,2 ..., col1k, row1kRevised first M of expression kth time ×
LCTie up matrix Q1kLine number, col1kIndicate the revised one M × L of kth timeCTie up matrix Q1kColumns, r' ∈ 1,2 ...,
row2k, h' ∈ { 1,2 ..., col2k, row2kIndicate the revised two M × L of kth timeCTie up matrix Q2kLine number, col2kTable
Show the revised two M × L of kth timeCTie up matrix Q2kColumns, r " ∈ { 1,2 ..., row3k, h " ∈ { 1,2 ..., col3k,
row3kIndicate the revised three M × L of kth timeCTie up matrix Q3kLine number, col3kIndicate the revised three M × L of kth timeCDimension
Matrix Q3kColumns, r " ' ∈ { 1,2 ..., row4k, h " ' ∈ { 1,2 ..., col4k, row4kIndicate kth time the revised 4th
M×LCTie up matrix Q4kLine number, col4kIndicate the revised four M × L of kth timeCTie up matrix Q4kColumns,Expression rounds up operation；a(θk,φ)r+h-1Expression incident direction is (θk, φ) signal guide arrow
Measure a (θk, φ) in the r+h-1 element, a (θk,φ)r'-h'+1Expression incident direction is (θk, φ) signal guide vector a (θk,
The r'-h'+1 element in φ), a (θk,φ)M+1+r”-h”Expression incident direction is (θk, φ) signal guide vector a (θk,φ)
In M+1+r "-h " a element, a (θk,φ)r”'+h”'-M-1Expression incident direction is (θk, φ) signal guide vector a (θk,φ)
In r " '+h " '-M-1 elements；θkIndicate the azimuth of Q incoming signal after kth time amendment, and after the 0th amendment Q it is a enter
Penetrate the azimuth angle theta of signal0For Q azimuth initial value of Q incoming signal.
The mutual coupling matrix properties of (4c) uniform circular array as described in (4b) are available, and kth time is revised nicely rounded
The mutual coupling Matrix C of battle arraykIt is with incident directionSignal guide vectorEquivalent substitution can be carried out, i.e.,Wherein, ckFor the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe first row before
LCThe L of a element compositionC× 1 dimensional vector；And then be calculated after kth time amendment the MUSIC spectrum inverse of Q incoming signal with
Jck, calculation expression are as follows:
Wherein,||||2Indicate that modulus value is squared again later
Operation.
(4d) is in order to solve the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe first row preceding LCA element composition
LC× 1 dimensional vector ck, add a linear restriction, it is assumed that self-impedance is 1 inside the array element of the mutual even matrix of uniform circular array, then Ck
(1,1)=1, i.e. eHck=1, wherein e be header element be 1, remaining element be 0 the dimensional vector of L × 1, that is, establish the following equation:
Wherein, subscript H indicates that conjugate transposition operation, s.t. indicate constraint condition.
The mutual coupling Matrix C of uniform circular array after kth time is corrected finally is calculatedkThe first row preceding LCA element composition
LC× 1 dimensional vector ck, expression formula are as follows:
ck=Gk -1e(eHGk -1e)-1
Due to the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe first row preceding LCThe L of a element compositionC× 1 tie up to
Measure ckFor the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe first row preceding LCThe L of a element compositionC× 1 dimensional vector, and
The mutual coupling Matrix C of uniform circular array after kth time amendmentkFor a multiple Cyclic Symmetry matrix, thus after kth time amendment uniform circular array it is mutual
Coupling Matrix CkIn element can be by the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe first row preceding LCA element composition
LC× 1 dimensional vector ckMiddle element determines completely.
Therefore, according to the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe first row preceding LCThe L of a element compositionC×
1 dimensional vector ck, the mutual coupling Matrix C of uniform circular array after kth time amendment is calculatedk。
Step 5, k is enabled to add 1, return step 3, until Jck-Jc(k-1)< △, then correcting iteration terminates, Jc(k-1)It indicates kth -1 time
The sum of the MUSIC spectrum inverse of Q incoming signal after amendment, △ indicate the threshold value of setting, and △ value is 0.0001 in the present embodiment；
And respectively by the mutual coupling Matrix C of uniform circular array after corresponding kth time amendment when correcting iteration stoppingk, it is denoted as the final mutual of uniform circular array
Even matrixThe azimuth angle theta of Q incoming signal after kth time corresponding when correcting iteration stopping is correctedk, it is denoted as Q incoming signal
Final bearing Indicate the final orientation of the q+1 incoming signal after amendment
Angle；And then the Q final incident directions of Q incoming signal are obtained, respectively φqIndicate pitch angle of the q+1 incoming signal relative to uniform circular array；Wherein,
For the final incident direction of desired signal.
Step 6, in the final mutual even matrix of the Q for having obtained Q incoming signal final incident directions and uniform circular arrayThe interference plus noise covariance matrix for starting to carry out uniform circular array afterwards reconstructs；Including the interference covariance square of uniform circular array
The noise covariance matrix of battle array reconstruct and uniform circular array reconstructs；And then the interference plus noise association of uniform circular array after reconstruct is calculated
Variance matrix.
Step 6 specifically includes following sub-step:
In the final incident direction for rejecting desired signal in the final incident direction of Q of (6a) from Q incoming signal, obtain
The final incident direction of Q-1 interference signal, respectively
In view of the error of Power estimation algorithm, azimuth evaluated error range is set as △ θ, such Q-1 interference signal
Angular regions can be expressed as
The final incident direction of i.e. Q-1 interference signal is all located atIt is interior, and Q-1 interference signal angular regionsPacket
Containing Q-1 discrete sampling point, each discrete sampling point respectively corresponds the final incident direction an of interference signal；It is dry at Q-1
Disturb signal angle regionL' discrete sampling point of interior any selection calculates covariance matrix, L'≤Q-1, then sum
The interference covariance matrix of uniform circular array after to reconstructI.e.
Wherein, union operation, b (θ are asked in ∪ expressionl',φl') it is Q-1 interference signal angular regionsInterior l' discrete
Steering vector at sampled point, l'=1,2 ..., L', and according to the final incident directions of the Q of Q incoming signal and uniform circular array
Final mutually even matrixThe steering vector b (θ, φ) of the desired signal after mutual coupling calibration is calculated,
Therefore the interference covariance matrix of uniform circular array after reconstruct is calculatedIts expression formula are as follows:
Wherein, R indicates the sample covariance matrix of uniform circular array, b (θl',φl') indicate Q-1 interference signal angular area
DomainSteering vector at interior the l' discrete sampling point is (θ with incident directionl',φl') signal guide vector value phase
Deng；And then complete the interference covariance matrix reconstruct of uniform circular array.
(6b) carries out the noise covariance matrix reconstruct of uniform circular array, in the ideal situation, assists to the sampling of uniform circular array
The M-Q small characteristic value difference obtained after variance matrix progress feature decomposition is equal, and value is exactly noise power-value.
But in a practical situation, M-Q small characteristic values are unequal, in order to calculate simplicity, in M-Q small characteristic value choosing
Characteristic value minimum value is taken, the noise power estimation value as uniform circular arrayAnd then uniform circular array is made an uproar after reconstruct is calculated
Sound covariance matrixI indicates that M × M ties up unit matrix.
(6c) carries out the interference plus noise covariance matrix reconstruct of uniform circular array: being assisted according to the interference of uniform circular array after reconstruct
Variance matrixWith the noise covariance matrix of uniform circular array after reconstructThe interference that uniform circular array after reconstructing is calculated adds
Noise covariance matrixIts expression formula are as follows:
Wherein, R indicates that the sample covariance matrix of uniform circular array, I indicate that M × M ties up unit matrix；And then it completes uniformly
The interference plus noise covariance matrix reconstruct of circle battle array.
Step 7, the vector that is eventually led to that desired signal is calculated isAnd according to uniform circular array after reconstruct
Interference plus noise covariance matrixThe adaptive of uniform circular array is calculated using linear constraint minimal variance (LCMV) criterion
The weight vector for answering Beam-former is w, and then completes the uniform circular array interference-plus-noise covariance based on iteration mutual coupling calibration
The Wave beam forming of matrix reconstruction designs.
Specifically, the vector that is eventually led to that desired signal is calculated is It is for incident directionSignal guide vector,For the final incident direction of desired signal, then utilize
Linear constraint minimal variance (LCMV) criterion finds out the weight vector w of the adaptive beam former of uniform circular array, expression formula are as follows:
Wherein, subscript -1 indicates that inversion operation, subscript H indicate conjugate transposition operation；And then it completes based on iteration mutual coupling
The Wave beam forming design of the uniform circular array interference plus noise covariance matrix reconstruct of correction.
Further verifying explanation is made to effect of the present invention by following emulation experiment.
(1) simulated conditions
What emulation experiment of the invention carried out under MATLAB software, in experiment of the invention, uniform circular array uses 10
A array element, the signal wavelength of Q incoming signal are set as 0.1 meter, the signal wavelength of adjacent array element spacing d and Q incoming signal
Ratio d/ λ be 0.5, each incoming signal is disposed as 30 ° relative to the pitch angle of uniform circular array, the orientation of desired signal
Angle is set as 95 °, and two interference signals are arranged, and the azimuth of two interference signals is respectively 50 ° and 140 °.
Specific algorithm parameter is as shown in the table:
(2) emulation content and interpretation of result
In order to illustrate the superiority of inventive algorithm, Fig. 2 to Fig. 5 gives the processing knot of other several beamforming algorithms
Fruit, including optimal beam forming device, sample matrix inversion (SMI) Beam-former, covariance matrix restructing algorithm and worst property
It can optimal method.
The horizontal axis of Fig. 2 indicates that input signal-to-noise ratio, the longitudinal axis indicate output Signal to Interference plus Noise Ratio；Fig. 2 indicates there are signal observation error,
Sampling number of snapshots is 30, the song that the output Signal to Interference plus Noise Ratio of several Beamforming Methods changes with desired signal input Signal to Interference plus Noise Ratio
Line.From Fig. 2 it will be seen that in the case where existing concurrently with mutual coupling and incoming signal observation error, common association side
Poor matrix reconstruction method performance sharply declines, and performance is even nothing like SMI method in the scene of low signal-to-noise ratio；Worst performance
It optimizes Beamforming Method and possesses preferable Robust Performance, but become Qiang Shiqi performance and theory most in desired signal power
The gap of the figure of merit is increasing；And the covariance matrix reconstructing method proposed by the present invention based on mutual coupling calibration is in high s/n ratio condition
Lower performance is very close to theoretially optimum value, and the performance of algorithm is declined under Low SNR, this is because believing in expectation
When number power is lower than noise level, misalignment can occur for DOA estimation, to influence the performance of Beam-former.
The horizontal axis of Fig. 3 (a) and Fig. 3 (b) indicates that sample number, the longitudinal axis indicate the output Signal to Interference plus Noise Ratio of Beam-former；
Fig. 3 (a) indicates in the simulation result there are signal observation error and when input signal-to-noise ratio is 20dB, and Fig. 3 (b) indicates to believe existing
Number observation error and simulation result when input signal-to-noise ratio is -5dB.Simulation result shows the input signal-to-noise ratio in desired signal
When relatively high, Beamforming Method performance proposed by the invention is substantially superior to other Beamforming Methods；In low signal-to-noise ratio
In the case where if can guarantee sample abundance, beamforming algorithm proposed by the present invention still has good performance.
The horizontal axis of Fig. 4 indicates that input signal-to-noise ratio, the longitudinal axis indicate output Signal to Interference plus Noise Ratio；Fig. 4 indicates that there is no signal observations to miss
Difference, sampling number of snapshots are 30, and the output Signal to Interference plus Noise Ratio of several Beamforming Methods is with desired signal input Signal to Interference plus Noise Ratio variation
Curve.From Fig. 4 it will be seen that only considering that the mutual coupling of uniform circular array causes desired signal and interference signal steering vector
Under conditions of mismatch, after this method mutual coupling calibration, the performance of Beam-former is optimal with theory in high s/n ratio
Value this is because this method is corrected just for mutual coupling factor, and eliminates sample covariance matrix almost without gap
In desired signal components, can achieve in the case where not considering other mismatch effects close to theoretical optimal performance.
The horizontal axis of Fig. 5 (a) and Fig. 5 (b) indicates that sample number, the longitudinal axis indicate the output Signal to Interference plus Noise Ratio of Beam-former；
Fig. 5 (a) indicates that the simulation result there is no signal observation error and when input signal-to-noise ratio is 20dB, Fig. 3 (b) indicate that there is no letters
Number observation error and simulation result when input signal-to-noise ratio is -5dB.The result shows that the on-job mutual coupling for considering uniform circular array causes
Under conditions of desired signal and interference signal steering vector mismatch, the performance of the method for the present invention, which is compared, considers signal observation error
It is much better.
In conclusion emulation experiment demonstrates correctness of the invention, validity and reliability.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (4)
1. a kind of radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method, which is characterized in that including with
Lower step:
Step 1, uniform circular array is determined, which includes M array element, there are Q signal source in uniform circular array setting range,
Q signal source emits Q incoming signal to uniform circular array, and the Q incoming signal includes 1 desired signal and Q-1 interference
Signal；
The sample covariance matrix R of uniform circular array is obtained, and feature point is carried out to the sample covariance matrix R of the uniform circular array
Solution, obtains M characteristic value；M, Q is respectively the positive integer for being greater than 0, and Q > 1, M indicate the uniform circular array element number of array that includes, and right
It is equal that the sample covariance matrix R of uniform circular array carries out the characteristic value number value obtained after feature decomposition；
Step 2, it calculates the signal MUSIC that incident direction is (θ, φ) to compose, then sets the mutual coupling matrix setup values of uniform circular array,
And then the Q azimuth initial value of Q incoming signal is obtained, respectivelyq∈{0,1,2,…,Q-
1 },Indicate the azimuth initial value of the q+1 incoming signal；
Initialization: enabling k indicate kth time amendment, and the initial value of k is 1；The mutual coupling matrix of uniform circular array is C after enabling kth time correctk,
And using Q azimuth initial value of Q incoming signal as the azimuth angle theta of Q incoming signal after the 0th amendment0；Setting is uniform
The mutual coupling matrix setup values of circle battle array are C0, C0=IM, IMIndicate that M × M ties up unit matrix；
Step 3, according to the mutual coupling Matrix C of uniform circular array after kth time amendmentkDirection of arrival is carried out respectively to Q incoming signal to estimate
Meter, incident direction is (θ after obtaining kth time amendmentk, φ) signal MUSIC compose PMUSIC(θk, φ) and kth time amendment after Q
The azimuth of a incoming signal；
Step 4, successively obtain the MUSIC spectrum inverse of Q incoming signal after kth time amendment and JckDefinition and calculating
Formula, and then the mutual coupling Matrix C of uniform circular array after kth time amendment is calculatedk；
Step 5, k is enabled to add 1, return step 3, until Jck-Jc(k-1)< Δ, then correcting iteration terminates, Jc(k-1)It indicates to repair for kth -1 time
Just after Q incoming signal MUSIC spectrum inverse sum, Δ indicate set threshold value, and respectively by amendment iteration stopping when
The mutual coupling Matrix C of uniform circular array after corresponding kth time amendmentk, it is denoted as the final mutual even matrix of uniform circular arrayIteration will be corrected
The azimuth of Q incoming signal, is denoted as the final bearing of Q incoming signal after corresponding kth time is corrected when stopping
Step 6, according to the final mutual even matrix of uniform circular arrayWith the final bearing of Q incoming signalReconstruct is calculated
The interference plus noise covariance matrix of uniform circular array afterwards
Step 7, the vector that is eventually led to of desired signal is calculated, and according to the interference plus noise association side of uniform circular array after reconstruct
Poor matrixThe weight vector that the adaptive beam former of uniform circular array is calculated is w, and then is completed mutual based on iteration
The Wave beam forming design of the uniform circular array interference plus noise covariance matrix reconstruct of coupling correction；
Wherein, in step 1, the Q incoming signal, further includes:
Q incoming signal is φ, φ={ φ relative to the pitch angle of uniform circular array0,φ1,…,φq,…,φQ-1, q ∈ 0,
1 ..., Q-1 }, φqIndicate pitch angle of the q+1 incoming signal relative to uniform circular array, and φ0、φ1、…、φq、…、
φQ-1Value difference is equal；φ0Indicate pitch angle of the desired signal relative to uniform circular array, Q-1 interference signal is relative to equal
The pitch angle of nicely rounded battle array is respectively φ1、φ2、…、φQ-1；
Feature decomposition, decomposed form are carried out to the sample covariance matrix R of the uniform circular array are as follows:
Wherein, R is the sample covariance matrix of uniform circular array, and dimension is M × M；ΛSIIt is respectively diagonal element for Q big characteristic value
The diagonal matrix that element is formed, USIThe desired signal formed for the corresponding feature vector of Q big characteristic value adds interference space, ΛN
It is respectively the diagonal matrix that diagonal element is formed, U for M-Q small characteristic valuesNFor the corresponding feature vector shape of M-Q small characteristic value
At noise subspace, subscript H indicate conjugate transposition operation, M, Q be respectively be greater than 0 positive integer, M > Q；M indicates nicely rounded
The element number of array that battle array includes carries out the characteristic value number obtained after feature decomposition with the sample covariance matrix R to uniform circular array
Value is equal；
In step 2, the incident direction is that the signal MUSIC of (θ, φ) composes PMUSIC(θ, φ), expression formula are as follows:
Wherein, θ indicates the azimuth of Q incoming signal, and φ indicates pitch angle of the Q incoming signal relative to uniform circular array, a
(θ, φ) is the signal guide vector that incident direction is (θ, φ), and C is the mutual coupling matrix of uniform circular array, UNFor M-Q small features
It is worth the noise subspace that corresponding feature vector is formed, subscript H indicates conjugate transposition operation；
The Q azimuth initial value for obtaining Q incoming signal, process are as follows:
Set the mutual coupling matrix setup values C of uniform circular array0, C0=IM, IMIndicate that M × M ties up unit matrix；By the mutual coupling of uniform circular array
Matrix setup values C0It substitutes into the signal MUSIC that incident direction is (θ, φ) and composes PMUSICIn (θ, φ) expression formula, and at 0 ° to 180 °
MUSIC spectral peak is searched in azimuth coverage, and then obtains the Q azimuth initial value of Q incoming signal, respectivelyQ ∈ { 0,1,2 ..., Q-1 },Indicate the azimuth initial value of the q+1 incoming signal；Wherein,
It sets in azimuth coverage as within the scope of 0 ° to 180 °；
In step 3, incident direction is (θ after the kth time amendmentk, φ) signal MUSIC compose PMUSIC(θk, φ), expression
Formula are as follows:
Wherein, θkIndicate the azimuth of Q incoming signal after kth time is corrected, φ indicates Q incoming signal relative to uniform circular array
Pitch angle, a (θk, φ) be incident direction be (θk, φ) signal guide vector, CkUniform circular array is mutual after correcting for kth time
Coupling matrix, UNFor the noise subspace that the corresponding feature vector of M-Q small characteristic value is formed, subscript H indicates conjugate transposition operation；
Set kth time amendment is searched in azimuth coverage after incident direction as (θk, φ) signal MUSIC compose PMUSIC(θk,φ)
MUSIC spectral peak, the azimuth for obtaining Q incoming signal after kth time amendment is θk, θk={ θ0k,θ1k,…,θqk,…,
θ(Q-1)k, q ∈ { 0,1 ..., Q-1 }, θqkIndicate the azimuth of the q+1 incoming signal after kth time is corrected；θ0kIndicate kth time
The azimuth of desired signal, θ after amendment1k,θ2k,…,θ(Q-1)kFor the azimuth of Q-1 interference signal after kth time amendment；Its
In, within the scope of 0 ° to 180 ° in setting azimuth coverage；
The sub-step of step 4 are as follows:
The mutual coupling Matrix C of uniform circular array after (4a) is corrected according to kth timek, define the MUSIC of Q incoming signal after kth time amendment
Spectrum it is reciprocal and be Jck, define expression formula are as follows:
Wherein,Indicate that incident direction isSignal guide vector, φqIndicate the q+1 incoming signal phase
For the pitch angle of uniform circular array, The q+1 incidence is believed after indicating kth time amendment
Number azimuth, | | | |2Indicate the squared operation again later of modulus value；CkThe mutual coupling matrix of uniform circular array after being corrected for kth time,
UNFor the noise subspace that the corresponding feature vector of M-Q small characteristic value is formed, subscript H indicates conjugate transposition operation；
(4b) determines the mutual coupling Matrix C of uniform circular array after kth time amendmentkBy the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe
Preceding L in a lineCA element is completely determining, Indicate downward floor operation；And determine kth time amendment
The mutual coupling Matrix C of uniform circular array afterwardskIt is (θ with incident directionk, φ) signal guide vector a (θk, φ) product, be equivalent into
Penetrating direction is (θk, φ) signal guide vector a (θk, φ) in M element composition M × LCTie up matrix Q [a (θk, φ)] with
The mutual coupling Matrix C of uniform circular array after kth time amendmentkThe preceding L of middle the first rowCThe L of a complete composition of elementC× 1 dimensional vector ckMultiply
Product, i.e. Cka(θk, φ) and=Q [a (θk,φ)]ck；
Wherein, ckFor the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe preceding L of middle the first rowCThe L of a element compositionC× 1 tie up to
Amount,d∈{0,1,…,LC- 1 }, cdkIndicate the mutual coupling of uniform circular array after kth time is corrected
Matrix CkThe d+1 element of middle the first row, subscript T indicate transposition operation；
Incident direction is (θk, φ) signal guide vector a (θk, φ) in M element composition M × LCTie up matrix Q [a (θk,
φ)] by the revised one M × L of kth timeCTie up matrix Q1k, kth time revised two M × LCTie up matrix Q2k, kth time amendment
Three M × L afterwardsCTie up matrix Q3kWith the revised four M × L of kth timeCTie up matrix Q4kAddition obtains, i.e. Q [a (θk, φ)]=
Q1k+Q2k+Q3k+Q4k, the revised one M × L of kth timeCTie up matrix Q1k, kth time revised two M × LCTie up matrix Q2k,
K revised three M × LCTie up matrix Q3kWith the revised four M × L of kth timeCTie up matrix Q4kIt is by incident direction respectively
(θk, φ) signal guide vector a (θk, φ) in element constitute, wherein kth time revised one M × LCTie up matrix Q1kIn
R row, h column element are Q1(r,h)k, the revised two M × L of kth timeCTie up matrix Q2kIn r' row, h' column element be
Q2(r',h')k, the revised three M × L of kth timeCTie up matrix Q3In r " row, h " column element be Q3(r”,h”)k, after kth time amendment
Four M × LCTie up matrix Q4In r " ' row, h " ' column element is Q4(r”',h”')k, expression formula is respectively as follows:
Wherein, r ∈ { 1,2 ..., row1k, h ∈ { 1,2 ..., col1k, row1kIndicate the revised one M × L of kth timeCTie up square
Battle array Q1kLine number, col1kIndicate the revised one M × L of kth timeCTie up matrix Q1kColumns, r' ∈ { 1,2 ..., row2k, h'
∈{1,2,…,col2k, row2kIndicate the revised two M × L of kth timeCTie up matrix Q2kLine number, col2kIndicate that kth time is repaired
Two M × L after justCTie up matrix Q2kColumns, r " ∈ { 1,2 ..., row3k, h " ∈ { 1,2 ..., col3k, row3kIndicate the
K revised three M × LCTie up matrix Q3kLine number, col3kIndicate the revised three M × L of kth timeCTie up matrix Q3kColumn
Number, r " ' ∈ { 1,2 ..., row4k, h " ' ∈ { 1,2 ..., col4k, row4kIndicate the revised four M × L of kth timeCTie up square
Battle array Q4kLine number, col4kIndicate the revised four M × L of kth timeCTie up matrix Q4kColumns, It indicates
Round up operation；a(θk,φ)r+h-1Expression incident direction is (θk, φ) signal guide vector a (θk, φ) in r+h-1
Element, a (θk,φ)r'-h'+1Expression incident direction is (θk, φ) signal guide vector a (θk, φ) in the r'-h'+1 member
Element, a (θk,φ)M+1+r”-h”Expression incident direction is (θk, φ) signal guide vector a (θk, φ) in M+1+r "-h " a member
Element, a (θk,φ)r”'+h”'-M-1Expression incident direction is (θk, φ) signal guide vector a (θk, φ) in r " '+h " '-M-1
Element；θkIndicate the azimuth of Q incoming signal after kth time amendment, and after correcting for the 0th time Q incoming signal azimuth angle theta0For
Q azimuth initial value of Q incoming signal；
(4c) determines the mutual coupling Matrix C of the revised uniform circular array of kth timekIt is with incident directionSignal guide vectorEquivalent substitution is carried out, i.e.,Wherein, ckFor uniform circular array after kth time amendment
Mutual coupling Matrix CkThe first row preceding LCThe L of a element compositionC× 1 dimensional vector；And then it is calculated after kth time amendment Q and enters
Penetrate the MUSIC spectrum inverse and J of signalck, calculation expression are as follows:
Wherein,|| ||2Indicate the squared operation again later of modulus value；
(4d) is established the following equation:
Wherein, e be header element be 1, remaining element be 0 the dimensional vector of L × 1, subscript H indicate conjugate transposition operation, s.t. table
Show constraint condition；
Then the mutual coupling Matrix C of uniform circular array after kth time is corrected is calculatedkThe first row preceding LCThe L of a element compositionC×1
Dimensional vector ck, expression formula are as follows:
ck=Gk -1e(eHGk -1e)-1
Finally according to the mutual coupling Matrix C of uniform circular array after kth time amendmentkThe first row preceding LCThe L of a element compositionC× 1 tie up to
Measure ck, the mutual coupling Matrix C of uniform circular array after kth time amendment is calculatedk。
2. a kind of radar covariance matrix based on iteration mutual coupling calibration as described in claim 1 reconstructs Beamforming Method,
It is characterized in that, in steps of 5, the final bearing of the Q incoming signalSpecifically:
The final bearing of Q incoming signal Indicate that q+1 enter after amendment
Penetrate the final bearing of signal；And then the Q final incident directions of Q incoming signal are obtained, respectivelyφqIndicate the q+1 incoming signal relative to
The pitch angle of uniform circular array；Wherein,For the final incident direction of desired signal.
3. a kind of radar covariance matrix based on iteration mutual coupling calibration as claimed in claim 2 reconstructs Beamforming Method,
It is characterized in that, in step 6, the interference plus noise covariance matrix of uniform circular array after the reconstructIt obtains process
Are as follows:
In the final incident direction for rejecting desired signal in the final incident direction of Q of (6a) from Q incoming signal, Q-1 is obtained
The final incident direction of a interference signal, respectively
Azimuth evaluated error range is set as Δ θ, and Q-1 interference signal angular regions are expressed as
The final incident direction of the Q-1 interference signal is all located atIt is interior, and Q-1 interference signal angular regionsInclude
Q-1 discrete sampling point, each discrete sampling point respectively correspond the final incident direction an of interference signal；It is interfered at Q-1
Signal angle regionL' discrete sampling point of interior any selection calculates covariance matrix, L'≤Q-1, then is summed to obtain
The interference covariance matrix of uniform circular array after reconstructIts expression formula are as follows:
Wherein, union operation, b (θ are asked in ∪ expressionl',φl') it is Q-1 interference signal angular regionsInterior the l' discrete sampling
Steering vector at point is (θ with incident directionl',φl') signal guide vector value it is equal；L'=1,2 ..., L'；
The noise covariance matrix of uniform circular array after reconstruct is calculated in (6b)I indicates that M × M ties up unit square
Battle array；Wherein,Indicate the noise power estimation value of uniform circular array；
(6c) is according to the interference covariance matrix of uniform circular array after reconstructWith the noise covariance matrix of uniform circular array after reconstructThe interference plus noise covariance matrix of uniform circular array after reconstructing is calculatedIts expression formula are as follows:
Wherein, R indicates that the sample covariance matrix of uniform circular array, I indicate that M × M ties up unit matrix.
4. a kind of radar covariance matrix based on iteration mutual coupling calibration as claimed in claim 3 reconstructs Beamforming Method,
It is characterized in that, in step 7, the vector that is eventually led to of the desired signal is It is for incident directionSignal guide vector,For the final incident direction of desired signal；
The weight vector w of the adaptive beam former of the uniform circular array, expression formula are as follows:
Wherein, subscript -1 indicates that inversion operation, subscript H indicate conjugate transposition operation.
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